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Scale Rules

Length Measures

Although shared words for units of measurement—typically body parts such as "hand" and "foot"—dated back to ancient times, the lengths of these units differed by local custom. By the 17th and 18th centuries, each European city had its own standard for length measures. Many places called this standard an "ell," although the spelling of the word varied. When this Museum opened in 1964, the curators collected original objects and reproductions to show how the mathematics of European daily life had been transported into American business and trade. One particular treasure is a pedometer made by Jacob Ramminger in Stuttgart, Germany, around 1600.

As national states unified formerly decentralized localities and as trade between different areas of Europe increased, governments made efforts to define national standards. The English lengths for the inch, foot, and yard were perhaps most prominent around the world, and they were utilized in the American colonies. In both the Articles of Confederation and the U.S. Constitution, the federal government reserved for itself the power to fix national weights and measures. Shortly thereafter, in the 1790s, scientists working for the French government developed the metric system, in which one meter represented one ten-millionth of the distance between the North Pole and the Equator. Although copies of metric standards were brought to the United States, Americans maintained a complicated relationship with the system of measurement. For instance, John Quincy Adams investigated the system in 1821; Charles Davies evaluated it again in 1867. Both men recommended that adoption of metric measurements be delayed since English units were so well established in American commerce.

In addition to examples of yard and meter standards from the 19th and 20th centuries and other efforts to promote the metric system, the collection has one of the rules Scottish Astronomer Royal Charles Piazzi Smyth distributed in an unsuccessful effort to prove that the system of measurement used by ancient Egyptians to build the pyramids correlated with the modern English system. There are also several rulers brought by the nation of Japan to the 1876 World's Fair to demonstrate its ability to adopt European units. Finally, this page contains some rules made by the notable American manufacturers Stanley and Lufkin and some rulers used in schools.

This white ceramic rule is stored in a wooden case lined with red felt, surrounded by wooden shapes to hold it in place and underneath a piece of plywood. The interior of the rule has two scales. The first is in red ink, divided to twentieths of a British inch, and numbered by ones from 0 to 25. A small scale dividing one inch into hundredths is to the left of this scale, and an extra 1/10" is at the right of the scale. The second scale is in black ink, divided to twentieths of a "pyramid inch," and numbered by ones from 0 to 25.

The scale is marked: SCALE OF BRITISH INCHES, (/) For residual error, at Temperature 68° F., see note on case. (/) SCALE OF 25 PYRAMID INCHES, OR 1 PYRAMID CUBIT. (/) at Temp. 68° F., = one ten-millionth of the earth's semi-axis of Rotation; with a Residual error, see note on case. The upper right corner of the scale is marked in red: B. & P. SCALE, No. 2. (/) May, 1867. The lower right corner of the scale is marked in black: MADE & DIVIDED BY (/) L. CASELLA. (/) 23. HATTON GARDEN, LONDON.

Two thermometers are screwed into the case on either side of the scale. The first is divided by single degrees Fahrenheit and numbered by tens from 20 to 140. The second is divided by two degrees Fahrenheit and numbered by tens from 10 to 150. Three-fourths of its tube has been missing since it arrived at the Museum in 1987. Both thermometers are marked: J. M. BRYSON (/) OPTICIAN (/) EDINBURGH. James Mackay Bryson (1824–1894), whose firm was known for making thermometers, came from a family of Edinburgh instrument makers and scientists.

A handwritten note on Royal Observatory of Edinburgh stationery is pasted inside the lid of the case. It reads, "1872 (/) The 'British Inches' of this scale, in Red divisional (/) lines, have been found by a preliminary Microscopic comp- (/) -arison to be true, for their whole 25 inch sum of (/) length, to within half the thickness of one of the division lines, (/) at the temperature of 68* Fah. The expansion for an in- (/) -crease of 1*F. on the whole 25 inches in length, = (/) = 0.00004 of an inch, nearly. (/)The above red British Inches are those in (/) terms of which the Earth has been measured in modern (/) times. The black Inches on the lower part of (/) the scale, are the Ancient Inches of the Great (/) Pyramid; in terms of which Inches, both the chief (/) measures of that Monument, and the modern (/) measures of the Earth, come out in round and (/) even numbers of fives and tens. They are, each (/) of them 0.001 of an inch longer than the British Inch. (/) P.S. (/) Ast. R. for Scotd."

Charles Piazzi Smyth (1819–1900) was Astronomer Royal of Scotland from 1846 to 1888. He did significant scientific work, including pioneering high-altitude observing and solar astronomy, but he was also obsessed with pyramidal numerology. From January to April, 1865, he and his wife, Jessica, made careful measurements of every surface of the Great Pyramid at Giza. He concluded that the pyramid was constructed using a measurement system he called "pyramid inches," which were each one ten-millionth of the earth's semi-axis of rotation. Since the pyramid inch was so close in length to the British inch, Smyth recommended that Great Britain retain the imperial system of weights and measures rather than adopt the metric system.

To visually demonstrate the agreement between the systems of measurement, Piazzi Smyth commissioned London instrument maker Louis Pascal Casella (1812–1897) to make rules like this one when Smyth published an account of his research in 1867. Since there is a discrepancy between the date on this rule and the note in the lid, the example owned by National Museums Scotland (online ID 000-190-004-745-C, catalog number T.1962.108) may be older than this instrument. By 1876 the Science Museum in London was also exhibiting a Casella scale of British and pyramid inches, donated by Piazzi Smyth. Library staff at Augustana College in Rock Island, Ill., were unable to determine how this object ended up at the college. Casella did not advertise the rule in his 1871 catalog.